In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.[1][2]
^(Conway 1995, p. 32, chapter 14: Conformal equivalence for simply connected regions, Definition 1.12: "A function on an open set is univalent if it is analytic and one-to-one.")
^(Nehari 1975)
and 22 Related for: Univalent function information
analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective. The function f : z ↦ 2 z + z 2 {\displaystyle...
Univalent may refer to: Univalentfunction – an injective holomorphic function on an open subset of the complex plane Univalent foundations – a type-based...
absolute value 1 {\displaystyle 1} . The Koebe function and its rotations are schlicht: that is, univalent (analytic and one-to-one) and satisfying f (...
mathematical functions Injective metric space – Type of metric space Monotonic function – Order-preserving mathematical functionUnivalentfunction – mathematical...
the univalentfunction itself. The Grunsky matrix and its associated inequalities were originally formulated in a more general setting of univalent functions...
family of holomorphic functions on the disk with positive real part. The Loewner semigroup generalizes the notion of a univalent semigroup. The Loewner...
analogues and generalizations". A holomorphic function on an open subset of the complex plane is called univalent if it is injective. One can prove that if...
Gabriel Koenigs, it gives a canonical representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the...
of univalent holomorphic functions on an open domain has a uniform limit on compacta, then either the limit is constant or the limit is univalent. If...
Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types. Types...
Titchmarsh's The Theory of Functions. Titchmarsh uses the terms 'simple' and 'schlicht' (function) in place of 'univalent'. Univalent means holomorphic and...
theory of modular forms and hypergeometric functions. It plays an important role in the theory of univalentfunctions, conformal mapping and Teichmüller spaces...
Languages. The MIT Press. function type at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program, Institute...
graph theory and to the theory of univalentfunctions: The conjecture on the coefficients of multivalent functions named after him is considered the most...
element of the second set; it is thus a univalent relation. This generalizes the concept of a (total) function by not requiring every element of the first...
between the work referred to as homotopy type theory, and that called the univalent foundations project. Although neither is precisely delineated, and the...
coefficients of univalentfunctions, Doklady of Soviet Academy of Sciences, 1965, v. 160, 4, 769 - 771. Milin I.M. On coefficients of univalentfunctions, Doklady...
in Hilbert space. ISBN 0-486-67748-6. Marvin Rosenblum and James Rovnyak (1994). Topics in Hardy Classes and UnivalentFunctions. ISBN 3-7643-5111-X....
Global Information